at a glance

0-12 Months

Can perceive numbers in simple ways (such as recognizing "twoness" and "threeness")

Sees that two amounts of continuous quantity, such as juice, is the same or different

13-36 Months

Can tell which of two quantities "looks like" it contains more

Learns first number words and uses number words to label toys while playing

Uses number words in the same order every time, even if the sequence is incorrect

Can learn, with practice, to say the number words from 1 to 10 and to point to objects while reciting the number words

37-48 Months

Begins to understand that numbers represent "how many" and that numbers later in the counting sequence represent bigger quantities

Counting improves and many children can count up to 20, 30, or even higher

Can represent the numbers up to five using finger patterns and can recognize the written digits 1 to 9

Uses a "one for me, one for you" strategy to equally distribute an even number of items (up to 10) between two people and recognizes that the number of items in each collection can be determined by counting only one collection

49-60 Months

Counting skills improve:

Can learn to count to 100

Starts counting forwards from numbers other than 1

Counts backwards from 10 and later from 20

Skip counts by 10s

Accuracy of object counting improves:

Accurately counts 9 objects at four years of age; accurately counts 28 or more objects at six years of age

Knows that it doesn't matter where you start counting when you are counting a set of objects

Knows that a counting word also represents the size of a collection

Conventional number-related skills improve:

Can learn to identify written one-digit number words and knows their cardinal values (e.g., can identify "three" and knows it means 3)

Learns the doubles facts to ten (e.g., 2+2; 3+3, etc.)

Correctly recognizes and verbally labels "one-half"

Engages in more advanced problem solving:

Develops more efficient strategies for addition and subtraction problems (e.g., using finger patters for numbers up to 10)

By kindergarten, can solve small number multiplication and division problems by using blocks to act out the problems